Question: Multiply the following complex numbers: $({-5}) \cdot ({4-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5}) \cdot ({4-i}) = $ $ ({-5} \cdot {4}) + ({-5} \cdot {-1}i) + ({0}i \cdot {4}) + ({0}i \cdot {-1}i) $ Then simplify the terms: $ (-20) + (5i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (5 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (5 + 0)i - 0 $ The result is simplified: $ (-20 - 0) + (5i) = -20+5i $